Quality Magazine

The Basics of X-Ray Tomography for Precision Measurement

April 26, 2011
This standalone, lead lined X-ray coordinate measuring machine exceeds OSHA safety requirements. Source: Werth Inc.


X-ray technology has existed for some time in the industry. We could detect voids in material, cracks in welds, but not dimensionally measure the parts. Recent developments in computer tomography (CT) now provide high precision measurements, even on internal features, using X-ray technology. This article will explain the basics of CT that make this possible. We start with an understanding of 2-D optical measurement and relate that to how X-ray is used to completely capture and measure 3-D geometries. After understanding the basic principals, we can explore the inherent challenges with x-ray and the technology developed to overcome them. The advent of this technology opens new possibilities for verification of advanced manufacturing methods.

2-D Optical Measurement

In 2-D optical measurement, positions of the parts’ edges are accurately located in relation to a datum. Edges are detected using a lens to magnify and project the part image onto a CCD chip with a pixel array. The light intensity that strikes each pixel produces electronic signals called gray scale values. Intense light, where the part does not block the light, produces high values. No light produces low values. Software evaluates where the pixels values dramatically change and establishes the locations of the edges. Algorithms compute the dimensional and spatial relationships of geometric elements to extract the part dimensions.

This, of course, is a simple explanation. It does not include optical system, subpixeling calculations, filtering, importance of lighting schemes, variable magnification for higher accuracy, and other techniques. These concepts were developed to overcome inherent errors in optical measurement. Without them, optical measurement is neither accurate and traceable nor consistent. Likewise, complex technical approaches were developed to provide x-ray with accuracy. However, these 2-D basics provide a starting point to understand 3-D X-ray measurement.



Pictured: An X-ray machine construction based on coordinate measuring machine principals.

3-D Computer Tomography: Machine Construction

Accurate tomography starts with machine construction, unlike X-ray machines of the past. A granite base provides the foundation for precision slides and scales from coordinate measuring machine design. It includes a high precision rotary axis. It can include an additional axis for a multi-sensor approach for the highest accuracy. Source: Werth Inc.

Gathering the Data: Point Cloud Reconstruction

The workpiece is placed on a high precision rotary axis between the X-ray tube and detector. The part is X-rayed and an X-ray projection is stored. The part is then rotated slightly and another X-ray is taken, and so on until the part is rotated through a complete 360 degrees with, typically, 400 or 800 X-ray projections. Software reconstructs these images with a known rotation angle into a voxel volume.

A voxel (from volumetric pixel) is like a 3-D pixel. Instead of gray scale light values, voxels represent density values inversely corresponding to the X-ray energy the workpiece absorbs. Evaluating where the voxel densities radically change determines the point locations on the inner and outer skins of the part. The use of calibrated gray scale algorithms provides sub voxel resolution and accuracy for the measurement points. Connecting those points with triangles produces an STL view resembling a CAD model view but representing the actual part.

A computer aided design (CAD) model is pictured. Source: Werth Inc.

Analysis of the Data: Comparison with CAD Data

Results of computer tomography (CT) are nothing like the 2D X-ray images we see at the dentist. Three dimensional point clouds are captured that accurately define the contours of the parts with extreme point density. With touch probes or other traditional sensors, several points are collected and geometric elements are calculated from them, lines, planes, circles etc. With dense 3-D point clouds, it is not necessary to select individual points for such calculations. To assign the points to the geometrical elements to which they belong, the point cloud is merged with the CAD model by a 3-D BestFit. A color-coded deviation plot graphically displays the distance of each actual point from the nominal surface on the computer aided design (CAD) model. It clearly indicates where the actual part is in and out of tolerance and by how much. This can be used, for example, to correct plastic injection molds.

Position, diameter, vector and form deviation are extracted by selecting the patches and measuring a cylinder. Source: Werth Inc.

Dimensional Measurement

Dimensional measurements are extracted by selecting patches on the CAD model and using standard coordinate measuring machine (CMM) software to measure them as geometric elements. The software uses all the points assigned to the corresponding patch of the CAD model to calculate the dimensions of the geometric elements and the related features. For example, the position, vector, diameter and form deviation are extracted by selecting the patches and therefore the related points from the point cloud to measure a cylinder.

Overcoming Resolution Limitations: Variable Magnification

The focal point size of the X-ray beam and the number of pixels of the X-ray sensor limit the resolution of computer tomography. Developments like variable magnification and raster tomography allows the machine to be adapted. Accurate machine mechanics to vary the distance between the emitter, detector and the workpiece provide the ability to use low magnification with a large field of view to capture large parts. It also provides zoom capability to capture smaller fields of view with higher magnification and resolution.

Shown here: raster tomography at higher magnification provides higher resolution and accuracy. Source: Werth Inc.

High Precision on Large Parts with Raster Tomography

Raster or grid scanning developed for 2-D optical measurement applied to 3-D tomography provides the ability to capture large parts at higher resolution. High magnification with its smaller field of view scans sections of parts at higher resolution. Precision machine design accurately repositions the workpiece and software developments precisely stitch the sections together into an accurate, complete 3-D point cloud making this possible.

Workpices also absorb low energy X-ray beams and higher energy beams at different rates, depending on material thickness. This results in so-called beam hardening artifacts. Source: Werth Inc.

Beam Hardening and Others

One effect is that the workpieces absorbs low energy X-ray beams and higher energy beams at different rates depending on material thickness. This results in so called beam hardening artifacts. This effect is partially reduced but not overcome with filters on the X-ray emitter. By limiting the spectrum of X-rays allowed to penetrate the part, more uniform patterns reflecting the actual geometry of the workpiece reach the detector. It is also not enough to linear compensate for material density calculated with geometrically uniform standards. Real workpieces vary with wall thicknesses and cavities and so do the artifacts. X-ray scattering, cone beam artifacts and other effects are also depend on the real part geometry and material and vary with the direction of beam penetration. The hardware and software design of sophisticated coordinate measuring machines with computed tomography limits these effects. An absolute accuracy of about 5 to 10 microns when measuring real parts is provided.

Pictured: Correction of the x-ray point cloud using a correction point cloud taken from the first article with a more accurate sensor. Source: Werth Inc.

Multi-Sensor Approach for the Highest Accuracy

Fairly high accuracy levels are achieved in computer tomography using the technology thus far explained. Further refinement in accuracy is achieved with a multi-sensor approach. A more accurate sensor, used on the first article only, captures an even more accurate point cloud. This more accurate point cloud, taken from the geometry of the actual part type and the X-ray point cloud is used to calculate a correction matrix. This correction matrix can be applied to all parts of the same type to fine tune the accuracy of the final 3-D point cloud. The geometries and tolerances of some parts make this essential to achieve the accuracies required.

Conclusions

By building on the technology that was developed for optical and multi-sensor measurement it is now possible to incorporate X-ray as a sensor for precision measurement. Advances in computer technology to rapidly process large amounts of data and new software developments open the door for this new technology. It will lead to new possibilities to reduce verification costs and meet the needs of manufacturing innovations.